Simplify the expression. $(-2x^{2}-6x)(3x^{3}-2x^{2}+5x)$
Solution: First use the distributive property. $ - 2 x^2 (3 x^3) - 2 x^2 (-2 x^2) - 2 x^2 (5 x) - 6 x (3 x^3) - 6 x (-2 x^2) - 6 x (5 x) $ Simplify. $ - 6x^{5} + 4x^{4} - 10x^{3} - 18x^{4} + 12x^{3} - 30x^{2} $ $-6x^{5}-14x^{4}+2x^{3}-30x^{2}$ Identify like terms. $ {- 6x^{5}} \color{#DF0030} {+ 4x^{4}} {- 10x^{3}} \color{#DF0030} {- 18x^{4}} {+ 12x^{3}} {- 30x^{2}} $ Add the coefficients. $ { -6x^{5}} \color{#DF0030} { -14x^{4}} {+ 2x^{3}} { -30x^{2}} $